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International Mathematics Competition
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IMC 2024 |
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IMC2024: Day 1, Problem 2
Problem 2. For \(\displaystyle n=1,2,\ldots\) let
\(\displaystyle S_n = \log\left( \sqrt[n^2]{1^1\cdot 2^2\cdot\ldots\cdot n^n}\right) - \log (\sqrt{n}), \)
where \(\displaystyle \log\) denotes the natural logarithm. Find \(\displaystyle \mathop{\lim}\limits_{n\to\infty} S_n\).
Sergey Chernov, Belarusian State University, Minsk
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